Question

1. choose the best answer.

apply the 30°-60°-90° triangle theorem. if the length of the shorter leg a of the triangle is 4 inches, what is the measure of the length of the longer leg b for the triangle to the nearest inch.
≈ 12 inches
4√2 inches
≈ 7 inches
3√4 inches

1. choose the best answer.

apply the 30°-60°-90° triangle theorem. what is the length of the shorter leg, a, and the longer leg, b, if the length of the hypotenuse, c, is 14 inches.
a =
b =

Explanation:

Problem 8

Step1: Recall 30-60-90 Triangle Ratios

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, the ratios of the sides are \(1:\sqrt{3}:2\) (shorter leg : longer leg : hypotenuse). So, shorter leg \(a\), longer leg \(b = a\sqrt{3}\), hypotenuse \(c = 2a\).

Step2: Substitute \(a = 4\)

Given \(a = 4\) inches, then \(b = 4\sqrt{3}\). Calculate \(4\sqrt{3}\approx4\times1.732\approx6.928\approx7\) inches.

Step1: Find Shorter Leg (\(a\))

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, hypotenuse \(c = 2a\). Given \(c = 14\) inches, solve for \(a\): \(a=\frac{c}{2}=\frac{14}{2} = 7\) inches.

Step2: Find Longer Leg (\(b\))

Longer leg \(b = a\sqrt{3}\). Substitute \(a = 7\), so \(b = 7\sqrt{3}\approx7\times1.732\approx12.124\) inches (or exact form \(7\sqrt{3}\)).

Answer:

\(\approx 7\) inches

Problem 9